Methods for physical retrieval of atmospheric profiles and direct assimilation of satellite radiances are reviewed on optimization theory basis. Advantages and disadvantages, differences and relationships between various methods are discussed. General strategies for optimal inversion of atmospheric profiles from satellite data are introduced. A few important special objective functions and search algorithms currently used in the atmospheric iteration inversion techniques are analyzed and compared. Typically, the Newton′ non-linear iteration method which is currently adopted as the core algorithm in the numerical weather analysis/forecast centers and in satellite data centers for their operational numerical products is discussed. Levenberg-Marquardt method and trust region method are proposed for atmospheric profiles retrieval which is capable of helping the improvement of the convergence properties of the inversion algorithm.